Finite Group Databasebeta

← #20256224

Subgroups — #20256224

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689851C211yesmaximal, characteristic, complemented
2#15689491C211yesmaximal, characteristic, complemented
3#15689482C211yesmaximal, characteristic
4#15689477C211yesmaximal, characteristic
5#15689430C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic
7#15689418C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic
9#15689342C211yesmaximal, characteristic
10#15689330C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689228C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic
14C4×#10625337C211yesmaximal, characteristic, complemented
15C47×#556C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094022—21no—
21#13094016C2211yescharacteristic
22#13094016C2211yescharacteristic
23#13094014—21no—
24#13094014—21no—
25C4×Dic94C2211yescharacteristic
26C4×Dic94C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28#13093989—21no—
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093955C2211yescharacteristic
32C4⋊(C47⋊C8)C2211yescharacteristic
33C4⋊(C47⋊C8)C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#124×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53C22⋊Q8×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47—21no—
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×Dic94—21no—
65C2×Dic94C2311yescharacteristic
66C4⋊C4×C47—21no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47D411yescharacteristic
71C4⋊C4×C47D411yescharacteristic
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C42×C47—21no—
80C42×C47—21no—
81C42×C47C2311yescharacteristic
82C42×C47C2311yescharacteristic
83C42×C47C2311yescharacteristic
84#10625337—22no—
85#10625337—22no—
86#10625335—22no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106Q8×C47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110Q8×C47—41no—
111D4×C47—21no—
112D4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128Dic94—21no—
129Dic94—42no—
130Dic94#4112yes—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47C22×D411yescharacteristic
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47C2×#4111yescharacteristic
149C4×C472−1+411yescharacteristic
150Dic47—22no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3377—471nomaximal, Sylow
155C2×C47—81no—
156C2×C47#54811yescharacteristic
157C2×C47#57511yescharacteristic
158C2×C47#57811yescharacteristic
159#557—471no—
160#556D4711yescharacteristic
161#491—471no—
162#489—471no—
163#488—471no—
164#479—471no—
165#478—471no—
166#477—471no—
167#464—471no—
168#464—471no—
169#462—471no—
170#446—471no—
171#441—471no—
172#440—471no—
173C4×Q16—471no—
174C47#337711yescharacteristic, complemented, Sylow
175C2×Q16—471no—
176C2×Q16—471no—
177C2×SD16—471no—
178C4⋊Q8—471no—
179C4⋊Q8—941no—
180C4⋊Q8C2×D4711yescharacteristic
181#126—21no—
182#126—21no—
183#125—471no—
184#125—471no—
185#125—941no—
186#125—941no—
187#124C2×D4711yescharacteristic
188#124C2×D4711yescharacteristic
189C22⋊Q8—21no—
190C4×Q8—471no—
191C4×Q8—471no—
192C4×Q8—471no—
193C4×Q8—941no—
194C4×Q8C2×D4711yescharacteristic
195C4×Q8C2×D4711yescharacteristic
196C4×Q8C2×D4711yescharacteristic
197C4×D4C2×D4711yescharacteristic
198#117—21no—
199#107—471no—
200#107—471no—
201#106—471no—
202C4⋊C8—471no—
203C4⋊C8—471no—
204C4⋊C8—471no—
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#103—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215#97—471no—
216#97—471no—
217C4×C8—471no—
218C2×Q8—471no—
219C2×Q8—941no—
220C2×Q8C22⋊D4711yescharacteristic
221C2×Q8C22×D4711yescharacteristic
222C2×Q8C22×D4711yescharacteristic
223C2×D4C22×D4711yescharacteristic
224C22×C4—21no—
225Q16—942no—
226Q16—942no—
227SD16—942no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8—471no—
231C2×C8—471no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4C22⋊D4711yescharacteristic
248C4⋊C4C22⋊D4711yescharacteristic
249C4⋊C4C22⋊D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C42—21no—
257C42—21no—
258C42—941no—
259C42—941no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C42C22×D4711yescharacteristic
263C42C22×D4711yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—41no—
270Q8—472no—
271Q8—941no—
272Q8—1882no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4C2×C22⋊D4711yescharacteristic
284C2×C4C2×C22⋊D4711yescharacteristic
285C2×C4C2×C22⋊D4711yescharacteristic
286C2×C4C2×C22⋊D4711yescharacteristic
287C2×C4C2×C22⋊D4711yescharacteristic
288C2×C4C2×C22⋊D4711yescharacteristic
289C2×C4C23×D4711yescharacteristic
290C8—941no—
291C8—941no—
292C8—941no—
293C8—941no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C22×C22⋊D4711yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—942no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4#41×D4711yescharacteristic
312C4#1309407111yescharacteristic
313C2—81no—
314C2#1568978011yescharacteristic
315C2#1568992111yescharacteristic
316C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3377
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689851C2semidirect
2. #15689491C2semidirect
5. #15689430C2semidirect
7. #15689418C2semidirect
10. #15689330C2semidirect
11. #15689254C2semidirect
12. #15689228C2semidirect
14. C4×#10625337C2semidirect
174. C47#3377semidirect